We know in a 2-D plain, $$$n$$$ point $$$(x_i,y_i)$$$ can uniquely determine a $$$n-1$$$ degree polynomial. Proof of it is to use Vandermonde Determinant.

I see a method to use 3-D Lagrange Interpolation Polynomial to determine a binary polynomial. It uses $$$(n+1)(m+1)$$$ points when the highest degree of $$$x,y$$$ is $$$n,m$$$. But why it work? I think there should be 2-D Vandermonde Determinant corresponding to it.

I find it hard to calculate the value of 2-D Vandermonde Determinant. Can Anyone help me to solve it or find a paper? Thanks :)